Along a roadway, each milepost has an attached synchronized clock, synchronized
with the clock at mile-zero. A 57 Chevy goes by at speed-v. Any one of the mileposts observes diminished clock face time on the dashboard clock passing by at
speed-v. This is time dilation.
What does the driver say? “I am not moving at speed-v. I am at the origin of
a co-ordinate system moving at speed-v.” But there is something he cannot say.
“My co-ordinate system has diminished clock face time.” He cannot be the observer of this effect. Straight from EDoMB-1905-Section §4.
What happens when the driver does velocity addition? This is in Section §5. Now the 57 Chevy is going past the mileposts at speed-w. And the mileposts observe ENHANCED clock face time on the dashboard clock going by at speed-w.
What can the driver say? He cannot say his speed-w is the speed of a co-ordinate system, a co-ordinate system where the Chevy is “at rest.” In a
sense, the Chevy is not on the milepost roadway. The Chevy is on a roadway which
is moving at negative speed-v underfoot. Speed-w is indeed the speed of the Chevy
with respect to the mileposts, but that is not the speed of Chevy with respect to
the Chevy’s own blacktop. The new co-ordinate system of the Chevy is the negative moving blacktop, not the Chevy itself at origin-zero.
So what does the driver say about enhanced clock time? For the velocity-addition-formula to work, the driver must put this enhanced clock to work
on the negatively moving blacktop. New time must be observed on the new axis.
This flatly contradicts Section §4.
At great length: https://dibdeck.blogspot.com/
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